Many systems involve multiplication processes. For example, population grows through reproduction; monetary investment grows through gains such as stock market gain. In another example, avalanche photodiodes (APDs) operate by multiplying carriers (e.g., electrons and holes) being accelerated by electric fields.
APDs are particularly useful for photon counting, which finds applications in remote sensing, optical communication encryption, astronomy, ballistic missile defense, and ladar applications.
APDs can be operated in the Geiger mode for photon counting. A Geiger-mode APD is biased above its breakdown voltage such that a majority of the carriers (electrons and holes) continue to impact ionize in a runaway fashion, until an external circuit quenches the otherwise infinitely increasing gain. The Geiger mode APDs have may high dark currents (counts), and thus can be more susceptible to space radiations.
It would be useful to simulate Geiger-mode APDs to predict their behaviors such as breakdown (runaway) probabilities as functions of biases. Monte Carlo simulations can potentially provide more insights into the breakdown behaviors of APDs than analytical models, and may be used in designing optimal APD structures. However, conventional Monte Carlo simulations trace every carrier throughout their transport and impact ionization processes. In the Geiger mode, the high gains of the carriers make conventional Monte Carlo simulations computationally prohibitive.